Anxious usually said when you the outcome or event to happen, while on the other hand worried is usually said when you don't want it to happen.
An example of these two in a sentence,
"I'm anxious to go on a date with my girlfriend after class." This is (usually) a good thing that you want.
"I'm worried that my girlfriend is going to dump me."
Normally you don't want your girlfriend to break up with you.